Question: Multiply.
Solution: $37 \times 6{,}903$ and $0.37 \times 690.3$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $37 \times 6{,}903$. Then we can estimate to place the decimal point in the product of $0.37 \times 690.3$. $\begin{aligned} 6{,}903&\\ \underline{ \times 37}&\\ 21}& {7} \times {3\text{ ones}}\\ 0}& {7} \times {0 \text{ tens}}\\ 6{,}300}& {7} \times{9\text{ hundreds}}\\ 42{,}000}& {7} \times {6\text{ thousands}}\\ 90}& {30} \times {3\text{ ones}}\\ 0}& {30} \times {0\text{ tens}}\\ 27{,}000}& {30} \times {9\text{ hundreds}}\\ \underline{+180{,}000}}& {30} \times {6\text{ thousands}}\\ 255{,}411 \end{aligned}$ $37 \times 6{,}903 = 255{,}411$ Let's estimate to place the decimal in $0.37 \times 690.3$. $\begin{aligned} 0.37 \times 690.3 &\approx 0.4 \times 700\\\\ &\approx 280 \end{aligned}$ Where can we place the decimal in $255{,}411$ to get a product close to $280$ ? $255.411 = 0.37 \times 690.3$